People often encounter objects that are perceptually indistinguishable from objects that they have seen before. When this happens, how do they decide whether the object they are looking at is something never before seen, or if it is the same one they encountered before? To identify these objects people surely use background knowledge and contextual cues. We propose a computational theory of identifying perceptually indistinguishable objects (PIOs) based on a set of experiments which were designed to identify the knowledge and perceptual cues that people use to identify PIOs. By identifying a PIO, we mean deciding which individual object is encountered, not deciding what category of objects it belongs to. In particular, identifying a PIO means deciding if the object just encountered is a new, never before seen object, or if it has been previously encountered, which previously perceived object it is. Our agent’s beliefs and reasoning are based on an intensional representation. Intensional representations model the sense of an object rather than the object referent, itself. The terms of our representation language, SNePS, denote mental entities. Some such entities are propositions; others are abstract ideas; others are the agent’s “concepts” or “ideas” of objects in the world. This is important for the task of identifying PIOs, because before the identification task is complete, the agent may have two mental entities, e1 and e2, that it might or might not conclude correspond to the same object in the world.